I What is the most general form of Hubble's law?

Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?

Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?

Any non-static spacetime (expanding or contracting) is always curved, so yes, the linear distance-recession rate relation (Hubble's law) always holds. The distance-redshift relation is non-linear and depends on the curvature of space (the spatial curvature-density parameter).